Question

(1 point) Rewrite the following using a single exponent.

Answer 1

we are given

$\frac{6^a6^a}{36^b} =36^x$

now, we can use property of exponent

$m^p *m^p=(m)^{2p}$

so, we can write as

$6^a *6^a=(6)^{a+a}$

$6^a *6^a=6^{2a}$

$6^a *6^a=(6^{2})^a$

$6^a *6^a=(36)^a$

now, we can plug back

$\frac{36^a}{36^b} =36^x$

we can use property of exponent as

$\frac{w^m}{w^n} =w^{m-n}$

we can write as

$36^{a-b} =36^x$

now, we can compare both sides exponents

and we will get

$x =a-b$................Answer