By LearningExpress Editors

Updated on Apr 22, 2013

To review these concepts, go to Powers and Exponents Study Guide.

**Powers and Exponents Practice Questions**

**Practice**

- Evaluate 6
^{4}. - Circle the expression that is NOT equivalent to 5 · 5 · 5 · 5.
5 · 4 (5 · 5)

^{2}5^{4}5 · 5^{3}625 - Evaluate
*cd*^{2}– 1 when*c*= –1 and*d*= –6. - The expression 4
^{–2}is equivalent to ____. - How can you simplify the expression 2
^{2}· 2^{3}? - Simplify:
*a*^{2}*b*·*ab*^{3} - Simplify:
- Simplify: (3
*xy*^{3})^{2}

**Solutions**

- 6
^{4}is equal to 6 · 6 · 6 · 6. When multiplied together, the result is 1,296. - 5 · 4 should be circled. This is equal to 20. The others are equivalent to 625.
- Substitute the values for the variables in the expression: (–1)(–6)
^{2}– 1Evaluate the exponent: (–1)(–6)

^{2}– 1Remember that (–6)

^{2}= (–6)(–6) = 36.Multiply the first term: (–1)(36) – 1

This simplifies to (–36) – 1. Evaluate by changing subtraction to addition and the sign of the second term to its opposite. Signs are the same, so add and keep the sign:

(–36) + (–1) = –37

- When you evaluate a negative exponent, take the reciprocal of the base and make the exponent positive. Therefore, 4
^{–2}is equivalent to , which simplifies to - When you multiply like bases, add the exponents. The expression 2
^{2}· 2^{3}is equivalent to 2^{2 + 3}, which simplifies to 2^{5}. - When you multiply like bases, add the exponents. The expression
*a*^{2}*b*·*ab*^{3}can also be written as*a*^{2}*b*^{1}·*a*^{1}*b*^{3}. Grouping like bases results in*a*^{2}*a*^{1}·*b*^{1}*b*^{3}. Adding the exponents gives*a*^{2 + 1}*b*^{1}+ 3, which is equal to*a*^{3}*b*^{4}, the simplified answer. - When you divide like bases, subtract the exponents. The expression then becomes
*x*^{6 – 3}, which simplifies to*x*^{3}. - When you raise a quantity to a power, raise each base to that power by multiplying the exponents. The expression (3
*xy*^{3})^{2}equals 3^{2}*x*^{2}*y*^{6}, which simplifies to 9*x*^{2}*y*^{6}. Another way to look at this problem is to remember that when a quantity is squared, it is multiplied by itself. The expression (3*xy*^{3})^{2}becomes (3*xy*^{3}) · (3*xy*^{3}). Multiply coefficients and add the exponents of like bases: 3 · 3*x*^{1+ 1}*y*^{3 + 3}simplifies to 9*x*^{2}*y*^{6}.

From Basic Math in 15 Minutes A Day. Copyright © 2008 by LearningExpress, LLC. All Rights Reserved.

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