Question

which expression is equivalent to (q^4)^-3/q^-15 for all values of q where the expressions is defined

f q^27
g 1/9^27
h q^3
j 1/9^3

Answer 1

Answer:

(h)q^3

Step-by-step explanation:

now,

(q^4)^-3/q^-15 =q^-12 × q^+15

=q^(-12+15)

=q^3

Answer 2

$\displaystyle \sf{ \frac{ {( {q}^{4} )}^{ - 3} }{ {q}^{ - 15} } = {q}^{3} }$

Given :

The expression

$\displaystyle \sf{ \frac{ {( {q}^{4} )}^{ - 3} }{ {q}^{ - 15} } }$

To find :

The expression which is equivalent for all values of q where the expressions is defined

$\displaystyle \sf{ f. \: \: {q}^{27} }$

$\displaystyle \sf{ g. \: \: \frac{1}{{q}^{27}} }$

$\displaystyle \sf{ h. \: {q}^{3} }$

$\displaystyle \sf{ i. \: \frac{1}{{q}^{3}} }$

Formula :

$\displaystyle \sf{1. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

‌$\displaystyle \sf{2. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{ {( {q}^{4} )}^{ - 3} }{ {q}^{ - 15} } }$

Step 2 of 2 :

Simplify the given expression

We use the formulas

$\displaystyle \sf{1. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

‌$\displaystyle \sf{2. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

Thus the given expression

$\displaystyle \sf{= \frac{ {( {q}^{4} )}^{ - 3} }{ {q}^{ - 15} } }$

$\displaystyle \sf{ = \frac{ { {q}^{} }^{ (- 3 \times 4)} }{ {q}^{ - 15} } }$

$\displaystyle \sf{ = \frac{ {q}^{ - 12} }{ {q}^{ - 15} } }$

$\displaystyle \sf{ = {q}^{ - 12 + 15} }$

$\displaystyle \sf{ = {q}^{ 3} }$

Hence the required option is h. q³

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