The exponent of c after simplifying 7 a 2 b 3-16 a 2 c 33 isA- 6B- 9C- 10D- 8

The correct option is B 9We know that for integers a(≠ 0),m and n, nbsp; (a^m)^n=a^mn. (7a^2b)^3( 16a^2c^3)^3=7^3(a^2)^3b^3× ( 16)^3(a^2)^3(c^3)^3 =7^3 × ( ...

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Standard VIII

Mathematics

Exponent of an Exponent

The exponent ...

Question

The exponent of $c$ after simplifying $(7 a^{2} b)^{3} (- 16 a^{2} c^{3})^{3}$ is ___

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Solution

The correct option is C 9
We know that for integers $a (\neq 0), m$ and $n,$
$(a^{m})^{n} = a^{m n} .$

$(7 a^{2} b)^{3} (- 16 a^{2} c^{3})^{3} = 7^{3} (a^{2})^{3} b^{3} \times (- 16)^{3} (a^{2})^{3} (c^{3})^{3}$
$= 7^{3} \times (- 16)^{3} \times a^{6} b^{3} \times a^{6} c^{9}$
$= (7^{3} \times {(- 16)}^{3}) a^{12} b^{3} c^{9} (∵ b^{m} \times b^{n} = b^{m + n})$

Thus, the exponent of $c$ in the given expression is 9.

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The exponent of c after simplifying (7a2b)3(−16a2c3)3 is ___

The correct option is C 9We know that for integers a(≠0),m and n, (am)n=amn. (7a2b)3(−16a2c3)3=73(a2)3b3×(−16)3(a2)3(c3)3 =73×(−16)3×a6b3×a6c9 =(73×(−16)3)a12b3c9 (∵bm×bn=bm+n) Thus, the exponent of c in the given expression is 9.

The exponent of $c$ after simplifying $(7 a^{2} b)^{3} (- 16 a^{2} c^{3})^{3}$ is ___