Algebraic Roots & Indices (AQA GCSE Maths: Foundation): Exam Questions

Simplify  $\frac{f^8{g}^3}{f^2{g}^6}$

Simplify  $3x^{-7}\times -6x^5$

${\left(3^4\right)}^n=3^{12}$

Find the value of $n$

$n=......................$

i) $2^8\times 2^m=2^6$ 

Work out the value of $m$.

$m$ = ................................................. [1]

ii) $5^n÷5^4=5^6$

Work out the value of $n$.

$n$ = ................................................. [1]

Simplify.

$5\times x^0$

[1]

Simplify $2x^3\times 3x^2$

Simplify.

$5m^2\times 2m^3$

(i) Find the value of $k$ when $x^{10}÷x^k=x^3$.

$k=$....................... [1]

(ii) Find the value of $n$ when $y^{10}\times y^n=1$.

$n=$......................... [1]

Simplify  $5a^6{b}^3\times 4a^{-4}{b}^4$

Simplify  $\frac{18x^8{y}^3}{6x^5{y}^7}$

${10000}^m\times {1000}^n$ can also be written in the form ${10}^y$

Show that $y=4m+3n$

Simplify

${\left(2f^3{g}^{-2}\right)}^5$

Simplify.

$4p^5{q}^3\times p^2{q}^{-4}$

Simplify $8t^8÷4t^4.$

Simplify  $x^3{y}^4\times x^5{y}^3$

Simplify

$w^7÷w^{-2}$

$4^w=\frac{1}{16}$

Find the value of $w$.

$w=$ ...............................

Simplify ${\left(a^2\right)}^{3x}$

Using your answer to part (a), simplify $2^x\times 4^{3x}$ giving your answer as a single power of 2