Question

simplify,giving the answer in the exponential form.[(-1/3)⁷]⁹×3⁶⁰​

Answer 1

Question 2:

Express the following in exponential form:

(i) 6 × 6 × 6 × 6 (ii) t × t

(iii) b × b × b × b (iv) 5 × 5 × 7 ×7 × 7

(v) 2 × 2 × a × a (vi) a × a × a × c × c × c × c × d

ANSWER:

(i) 6 × 6 × 6 × 6 = 64

(ii) t × t= t2

(iii) b × b × b × b = b4

(iv) 5 × 5 × 7 × 7 × 7 = 52 × 73

(v) 2 × 2 × a × a = 22 × a2

(vi) a × a × a × c × c × c × c × d = a3 c4 d

Answer 2

Answer -

$\:\:\:\:\leadsto\boxed{\bf{(-3)^{123}}}$

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Solution -

$\:\:\:\:\implies\sf{\{( - \frac{1}{3})^{7}\}^{ - 9} \times 3 ^{60} }$

$\:\:\:\:\implies\sf{\{(-3)^{-7}\}^{ - 9} \times 3 ^{60} }$

$\:\:\:\:\implies\sf{(-3)^{-7 \times - 9} \times 3 ^{60} }$

$\:\:\:\:\implies\sf{(-3)^{63} \times 3 ^{60} }$

$\:\:\:\:\implies\sf{(-3)^{63+60} }$

$\:\:\:\:\implies\boxed{\bf{(-3)^{123}}}$

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Laws of exponents -

Product -- $\bf{a^{x}\times a^{y}=a^{x+y}}$

Quotient -- $\bf{a^{x}÷ a^{y}=a^{x-y}}$

Power -- $\bf{(a^x)^y=a^{xy}}$

Zero Exponent -- $\bf{a ^ 0 = 1}$

Negative Exponent -- $\bf{a^{-x}=\frac{1}{a^{x}}}$