Simplify 45^(-3/2)*45^2

$45^{- \frac{3}{2}} \cdot 45^{2}$

Step 1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$45^{- \frac{3}{2} + 2}$

Step 2

To write $2$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$45^{- \frac{3}{2} + 2 \cdot \frac{2}{2}}$

Step 3

Combine $2$ and $\frac{2}{2}$ .

$45^{- \frac{3}{2} + \frac{2 \cdot 2}{2}}$

Step 4

Combine the numerators over the common denominator.

$45^{\frac{- 3 + 2 \cdot 2}{2}}$

Step 5

Simplify the numerator.

Multiply $2$ by $2$ .

$45^{\frac{- 3 + 4}{2}}$

Add $- 3$ and $4$ .

$45^{\frac{1}{2}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$45^{\frac{1}{2}}$

Decimal Form:

$6.70820393 \dots$