What is 45^{-3/2}*45^2 ?

The solution to 45^{-3/2}*45^2 is 3*5^{1/2}

Popular >

simplify 45^{-3/2}*45^2

simplify

4 5^{- \frac{3}{2}} \cdot 4 5^{2}

3 \cdot 5^{\frac{1}{2}}

Decimal Notation

6.70820 \dots

Solution steps

4 5^{- \frac{3}{2}} \cdot 4 5^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

4 5^{- \frac{3}{2}} \cdot 4 5^{2} = 4 5^{- \frac{3}{2} + 2}

= 4 5^{- \frac{3}{2} + 2}

- \frac{3}{2} + 2 = \frac{1}{2}

= 4 5^{\frac{1}{2}}

Prime factorization of

45 : 3^{2} \cdot 5

= (3^{2} \cdot 5)^{\frac{1}{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3^{2} \cdot 5)^{\frac{1}{2}} = (3^{2})^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

= (3^{2})^{\frac{1}{2}} \cdot 5^{\frac{1}{2}}

(3^{2})^{\frac{1}{2}} = 3

= 3 \cdot 5^{\frac{1}{2}}

x^{4} - 4 x^{3} + x^{2} - 4 x

\frac{7}{3} + \frac{5}{2}

(\frac{- 1 + 4 x ^{\frac{4}{3}}}{4 x ^{\frac{2}{3}}})^{2}

∣ x - 2 ∣ \leq 6

(- 1)^{- 1} (- 1)^{0} (- 1)