Question

Simplify and express the answer in exponential form

1.$[{\left(3^2\right)}^4\times \left({15}^3\right)]÷5^3$

2.$[{\left(3^2\right)}^5\times 7^{10}\times 2^{10}]$

3.$\frac{9^3\times a^7\times {15}^2\times 8^0\times b^5}{3^4\times a^5\times 5^3\times b^2}$

4.$\left[\right(-3{)}^5\times (-3{)}^2]÷(-3{)}^7$

Answer 1

BODMAS

Bracket of Division, multiplication, addition, substraction.

1)

$=\left[\right((3{)}^2{)}^4\times (\left(15{)}^3\right)]÷5^3$ $[\because (a\times b{)}^n=a^n\times b^n]$

$=[3^8\times 3^3\times 5^3]÷5^3$

$=3^{11}$

2)

$\left[\right((3{)}^2{)}^5\times 7^{10}\times 2^{10}]$ $[\because (a^m{)}^n=a^{m\times n}]$

$=[3^{10}\times 7^{10}\times 2^{10}]$

$=[3\times 7\times 2{]}^{10}={42}^{10}$

3)

$\frac{9^3\times a^7\times {15}^2\times 8^0\times b^5}{3^4\times a^5\times 5^3\times b^2}$ $[\because a^0=1]$

$\frac{(3^2{)}^3\times a^7(5\times 3{)}^2\times 1\times b^5}{3^4\times 5^3\times a^5\times b^2}$

$\frac{3^8\times 5^2\times a^7\times b^5}{3^4\times 5^3\times a^5\times b^2}=\frac{3^4}{5}\times a^2\times b^3$

4)

$\frac{(-3{)}^5\times (-3{)}^2}{(-3{)}^7}=\frac{(-3{)}^7}{(-3{)}^7}=1$