Question

Choose an equivalent expression for two fifths raised to the fourth power times two fifths raised to the third power all raised to the second power.
two fifths raised to the fourteenth power
two fifths raised to the twenty fourth power
four twenty fifths raised to the fourteenth power
four twenty fifths raised to the twenty fourth power

Answer 1

The equivalent expression is two fifths raised to the fourteenth power. Option A

How to determine the expressions

From the information given, we have;

• two fifths raised to the fourth power times two fifths raised to the third power all raised to the second power

This could be written as;

$((\frac{2}{5} )^4 * (\frac{2}{5}^3) )^2$

Solve the index forms using multiplicative addition

$((\frac{2}{5} )^ 4^+^3)^2$

Add the powers

$((\frac{2}{5} )^7)^2$

Expand the powers

$(\frac{2}{5} )^7^*^2$

(2/ 5)^14

This means two fifths raised to the fourteenth power

Thus, the equivalent expression is two fifths raised to the fourteenth power. Option A

Learn more about index forms here:

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