What is (5m^6n^3)(6m^4p^4)(1/3 mp^5) ?

The solution to (5m^6n^3)(6m^4p^4)(1/3 mp^5) is 10m^{11}n^3p^9

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simplify (5m^6n^3)(6m^4p^4)(1/3 mp^5)

simplify

(5 m^{6} n^{3}) (6 m^{4} p^{4}) (\frac{1}{3} m p^{5})

10 m^{11} n^{3} p^{9}

Solution steps

(5 m^{6} n^{3}) (6 m^{4} p^{4}) (\frac{1}{3} m p^{5})

Apply exponent rule:

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

m^{6} m^{4} m = m^{6 + 4 + 1}

= 5 n^{3} \cdot 6 p^{4} \frac{1}{3} m^{6 + 4 + 1} p^{5}

Add the numbers:

6 + 4 + 1 = 11

= 5 n^{3} \cdot 6 p^{4} \frac{1}{3} m^{11} p^{5}

Apply exponent rule:

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

p^{4} p^{5} = p^{4 + 5}

= 5 n^{3} \cdot 6 \cdot \frac{1}{3} m^{11} p^{4 + 5}

Add the numbers:

4 + 5 = 9

= 5 n^{3} \cdot 6 \cdot \frac{1}{3} m^{11} p^{9}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 5 n ^{3} \cdot 6 m ^{11} p ^{9}}{3}

Multiply the numbers:

1 \cdot 5 \cdot 6 = 30

= \frac{30 m ^{11} n ^{3} p ^{9}}{3}

Divide the numbers:

\frac{30}{3} = 10

= 10 m^{11} n^{3} p^{9}

(5.2 \cdot 1 0^{15}) (6.5 \cdot 1 0^{- 8})

(3 e^{3 x}) (x e^{3 x})

What is (5m^6n^3)(6m^4p^4)(1/3 mp^5) ?
The solution to (5m^6n^3)(6m^4p^4)(1/3 mp^5) is 10m^{11}n^3p^9