Recent questions tagged simplify

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Simplify \((\sqrt{5}+4)^2-\sqrt{45}\) without using calculator
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Simplify \(\frac{3^x \times 3^{x-2}}{9^{x-3}}\)
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Simplify the following expression \( \sqrt{125}+3 \sqrt{2}-\frac{16}{\sqrt{32}}-\sqrt{20} \)
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Simplify the following expressions: \( 6 p-4+2(2 p+3) \)
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Simplify \(\sqrt[15]{243}\)
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Simplify \( (x+5)(x+2) \)
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Simplify the complex expression\[(2-3 i)(-2+i)\]
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Simplify the complex number \(5(3-2 i)+2 i(4+6 i)\)
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SImplify \((3 x) /\left(x^2+3\right)-(2 x) /\left(x^2+1\right)\)
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Factorise fullya) \(6 x y-2 x\)b) \(x^2(y+3)-(y+3)\)c) \(4 x^2-y^2\)d) \(x^2-11 x+18\)
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Given the function \(h(p)=p^2+2 p\), solve for \(h(p)=3\).
221
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Solve the equation.\[\log _3(2 x-3)=\log _3(x+5)\]
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Simplify \(\frac{3^{2 x} \cdot 27^{x-1}}{9^{2 x+2}}\)
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Simplify \(2^x \cdot 8^{x+1}\)
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Simplify \(a^{2 x} \cdot a^{3 x+1}\)
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Rewrite \(5^3=125\) as a logarithmic equation.
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Rewrite \(\log _3 9=2\) as an exponential equation.
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Simplify \(8 r^2+5 r^2=\)
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Calculate \(\frac{2}{x}+\frac{3}{x}\) and simplify the answer if necessary
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Simplify the algebraic expression \(2x+3y-4x-4xy-5x+4x^2-xy^2\)
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a. Simplify \(\dfrac{3^{x+1}-3^x}{3^x}\)b. Hence or otherwise simplify \(\dfrac{3^{x+1}-3^x}{m \cdot 3^x+2^2 3^x}-\dfrac{3 m-12}{m^2-16}\)
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Simplify by rationalising the denominator (show all working without using a calculator)\(\dfrac{3}{\sqrt{7}-\sqrt{5}}\)
273
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Without using a calculator, simplify: \(\dfrac{(2 a)^{-2} \times 3 a^{-5}}{\left(a^3 b^{\frac{1}{2}}\right)^2 \times(a b)^0}\)
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Without using a calculator \(\dfrac{6^{2 m} \times 4^{-m}}{\left(3^m\right)^2}\)
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Simplify without using a calculator \(\dfrac{\sqrt{9^{x+2}}-\sqrt{9^{x-2}}}{3^{x-3}}\)
258
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Solve for \(x\) \[ 4 x^2-4 x-1=0 \] (leave your answers in simplest surd form)
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How do you simplify an expression with exponents?
248
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Given:(i) \(\mathrm{A}=60^{\circ}\) and \(\mathrm{B}=30^{\circ}\)(ii) \(\mathrm{A}=110^{\circ}\) and \(\mathrm{B}=50^{\circ}\)(iii) \(\mathrm{A}=225^{\circ}\) and \(\math...
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Simplify the following trigonometric expressions:(a) \(\sin 210^{\circ}-\tan 120^{\circ} \cdot \cos 330^{\circ}\)(b) \(\dfrac{\cos 410^{\circ}}{\sin 40^{\circ}}\)(c) \(\t...
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Simplify the following:(a) \(\dfrac{\cos \left(180^{\circ}-\theta\right) \cdot \cos \left(90^{\circ}-\theta\right)}{\sin \left(90^{\circ}+\theta\right) \cdot \sin \left(-...
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Solve \(3 \log x=\log 27\)
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Simplify \(\frac{\log 16}{\log 4}\)
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SImplify \(\dfrac{\left(\log _2 8\right)^2}{\log _2 8^2}\)
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simplify \(\log _3 \sqrt{27}\)
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Simplify \(\log _3 \frac{1}{27}\)
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simplify \(-\log 4-\log 25\)
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Simplify using laws of logs \(\log _3 27-\log _3 3\)
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Simplify \(\log _9 27+\log _9 3\)
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Solve for \(n\) in \(\frac{1}{128}=2\left(-\frac{1}{2}\right)^n\)
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Solve for \(n\) in the equation \(\dfrac{1}{81}=\left(-\dfrac{1}{3}\right)^n\)
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Solve for \(n: \dfrac{1}{81}=\left(\dfrac{1}{3}\right)^n\)
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Simplify the expression: \(2x + 3x\)
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Use the properties of logarithms to simplify the expression log base 5 of 25 + log base 5 of 125.
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Simplify the expression log base 10 of 100.
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Simplify the expression log base 2 of 32.
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Simplify the expression \(5x + 3y - 2x + 4y.\)
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Factorise fully:\(1. \quad 10 t^2-5 t\)\(2. \quad 81-100 a^2\) \(3. \quad x^2+5 x+6\)
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Calculate \(8\left(\frac{1}{8}-\sqrt{\frac{1}{16}}\right)\)
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Calculate \(\sqrt{\frac{9}{16}} \div \sqrt{\frac{1}{4}}\).
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