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

The solution to 45^{3/2}*45^2 is 273375*5^{1/2}

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

simplify

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

273375 \cdot 5^{\frac{1}{2}}

Decimal Notation

611285.08334 \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{7}{2}

= 4 5^{\frac{7}{2}}

Prime factorization of

45 : 3^{2} \cdot 5

= (3^{2} \cdot 5)^{\frac{7}{2}}

Apply exponent rule:

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

(3^{2} \cdot 5)^{\frac{7}{2}} = (3^{2})^{\frac{7}{2}} \cdot 5^{\frac{7}{2}}

= (3^{2})^{\frac{7}{2}} \cdot 5^{\frac{7}{2}}

(3^{2})^{\frac{7}{2}} = 2187

= 2187 \cdot 5^{\frac{7}{2}}

5^{\frac{7}{2}} = 5^{3} \cdot 5^{\frac{1}{2}}

= 5^{3} \cdot 2187 \cdot 5^{\frac{1}{2}}

5^{3} = 125

= 2187 \cdot 125 \cdot 5^{\frac{1}{2}}

Multiply the numbers:

2187 \cdot 125 = 273375

= 273375 \cdot 5^{\frac{1}{2}}

(\frac{3}{2})^{- 3}

2 j + 2 j = 16

330 \cdot \frac{π}{180}

\frac{1}{( a - b ) ( a - c )} + \frac{1}{( b - c ) ( b - a )} + \frac{1}{( c - a ) ( c - b )}

a^{2} - 2 a + 1