Question

Simplify the following and express the answer in exponent

1). $7^3\times 7^2\times 7^9$

2). $(8{)}^{15}÷(8{)}^{12}$

3). $(5{)}^4\times (5{)}^4÷(5{)}^2$

4). $p^4\times q^4\times r^4$

Answer 1

(1)

$7^3\times 7^2\times 7^9$

$={\left(7\right)}^{(3+2+9)}$ ( $x^a\times x^b=x^{a+b}$ )

$=7^{14}$

(2)

$8^{15}÷8^{12}$

$={\left(8\right)}^{(15-12)}$ $(\frac{x^a}{x^b}=x^{a-b})$

$=8^3$

(3)

$5^4\times 5^4÷5^2$

$=5^4\times {\left(5\right)}^{(4-2)}$

$=5^4\times 5^2$

$=5^{4+2}$

$=5^6$

(4)

$p^4\times q^4\times r^4$

$={(p\times q\times r)}^4$

$={\left(pqr\right)}^4$