Question

Drag the tiles to the correct boxes to complete the pairs.

Answer 1

QUESTION 1

The given expression is:

$(2^2)^2\times (2^3)^{-3}$

Apply this property;

$(a^m)^n=a^{mn}$

to obtain;

$2^4\times 2^{-9}$

Recall and use the property: $a^m\times a^n=a^{m+n}$.

$2^{4+-9}=2^{-5}$

$\boxed{2^{-5}}\to \boxed{(2^2)^2\times (2^3)^{-3}}$

QUESTION 2

We have

$2^4\times (2^2)^{-2}$

We apply this property to get;

$(a^m)^n=a^{mn}$

$2^4\times 2^{-4}$

The bases are the same so we add the exponents

$2^4\times 2^{-4}=2^{4+-4}$

$2^{4+-4}=2^0=1$

$\boxed{1}\to \boxed{2^4\times (2^2)^{-2}}$

QUESTION 3

We have

$(-2^{-4})^{-2}\times (2^2)^0$

Multiply the exponents;

$2^{8}\times 2^0$

$2^{8}\times1=2^{8}$

$\boxed{2^{8}}\to \boxed{(-2^{-4})^{-2}\times (2^2)^0}$

QUESTION 4

The given expression is

$(-2^2)^{-6}\div (2^{-5})^{-4}$

We multiply the exponents to get;

$2^{-12}\div 2^{20}$

Subtract the exponents to get;

$2^{-12-20}= 2^{-32}$

$\boxed{2^{-32}}\to \boxed{(-2^2)^{-6}\div (2^{-5})^{-4}}$