Question

Using laws of e×ponents, simplify and write the answer in e×ponential form:
(i) 3²× 3⁴× 3⁸
(ii) 6¹⁵÷ 6¹⁰
(iii) a³ × a²
(iv) 7×x 7²
(v) (5²)³ ÷ 5³
(vi) 2⁵× 5⁵
(vii) a⁴× b⁴
(viii) (3⁴)³
(ix) (2²⁰÷ 2¹⁵) × 2³
(x) 8t ÷ 8²​

Answer 1

(i) 3²× 3⁴× 3⁸

$\boxed{\sf{Formula: a^p\times a^q\times a^r=a^{p+q+r}}}$

$\sf{\implies 3^2\times 3^4\times 3^8=3^{2+4+8}=\boxed{3^{14}}}$

(ii) 6¹⁵÷ 6¹⁰

$\boxed{\sf{Formula: \dfrac{a^p}{a^q}=a^{p-q}}}$

$\sf{\implies \dfrac{6^{15}}{6^{10}}=6^{15-10}=\boxed{6^{5}}}$

(iii) a³ × a²

$\boxed{\sf{Formula: a^p\times a^q=a^{p+q}}}$

$\sf{\implies a^3\times a^2=a^{3+2}=\boxed{a^{5}}}$

(v) (5²)³ ÷ 5³

$\boxed{\sf{Formula: \dfrac{(a^p)^n}{a^q}=a^{pn-q}}}$

$\sf{\implies \dfrac{(5^{2})^3}{5^{3}}=5^{6-3}=\boxed{5^{3}}}$

(vi) 2⁵× 5⁵

$\boxed{\sf{Formula: a^p\times b^p=(a\times b)^{p}}}$

$\sf{\implies 2^5\times 5^5=(2\times5)^5=\boxed{10^{5}}}$

(vii) a⁴× b⁴

$\boxed{\sf{Formula: a^p\times b^p=(a\times b)^{p}}}$

$\sf{\implies a^4\times b^4=(a\times b)^4=\boxed{ab^{5}}}$

(viii) (3⁴)³

$\boxed{\sf{Formula: (a^p)^n=a^{pn}}}$

$\sf{\implies (3^4)^3=3^{4\times 3}=\boxed{3^{12}}}$

(ix) (2²⁰÷ 2¹⁵) × 2³

$\boxed{\sf{Formula: \dfrac{a^p}{a^q}\times a^r=a^{p-q+r}}}$

$\sf{\implies \dfrac{2^{20}}{2^{15}}\times 2^3=2^{20-15+3}=\boxed{2^{8}}}$

(x) 8t ÷ 8²​

$\boxed{\sf{Formula: \dfrac{at}{a^2}=\dfrac{t}{a}}}$

$\sf{\implies \dfrac{8t}{8^2}=\boxed{\dfrac{t}{8}}}$