Question

Find the value of p in the given expression:(-3)^p-3 * {-3)^-3p+1 = (-3)^5

Answer 1

The value of p is -7/2.

Given:

• ${( - 3)}^{ p - 3} \times {( - 3)}^{ - 3p + 1} = ( { - 3)}^{5}$

To find:

• Find the value of p in the given expression.

Solution:

Formula to be used:

1. $\bf {a}^{n} \times {a}^{m} = {a}^{m + n}$
2. When base are same we can compare power.

Step 1:

Apply formula in LHS.

${( - 3)}^{ p - 3 - 3p + 1} = ( { - 3)}^{5}$

or

${( - 3)}^{ - 2p - 2} = ( { - 3)}^{5}$

Step 2:

Compare the powers; as base are same in both sides.

$- 2p - 2 = 5$

or

$- 2p = 5 + 2$

or

$\bf \red{p = \frac{ - 7}{2}}$

Thus,

Value of p is -7/2.

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