**Adding/Subtracting Fractions with Variables and Exponents Practice Problems**

### Set 1: Adding/Subtracting Fractions with Variables and Exponents

To review addition and subtraction of fractions with variables in one or more of the denominators, go to Adding/Subtracting Fractions Help

**Practice**

**Solutions**

### Set 2: Exponent Properties 5 & 6 - Adding/Subtracting Fractions with Variables and Negative Exponents

To review Exponent Properties 5-6, go to Adding/Subtracting Fractions Help

**Practice**

Use Properties 1–6 to rewrite without a negative exponent.

**Solutions**

**Set 3: Exponent Properties 7 & 8 - Adding/Subtracting Fractions with Variables and Exponents with Products and Quotients**

To review how to simplify expressions and eliminate negative exponents, go to Adding/Subtracting Fractions Help.

**Practice**

Simplify and eliminate any negative exponents.

1. ( *xy* ^{3} ) ^{2} =

2. (3 *x* ) ^{–3} =

3. (2 *x* ) ^{4} =

4. (3( *x* –4)) ^{2} =

5. 6(2 *x* ) ^{3} =

6. 6 *y* ^{2} (3 *y* ^{4} ) ^{2} =

7. (5 *x* ^{2} *y* ^{4} *z* ^{6} ) ^{2} =

**Solutions**

1. ( *xy* ^{3} ) ^{2} = *x* ^{2} ( *y* ^{3} ) ^{2} = *x* ^{2} *y* ^{6}

3. (2 *x* ) ^{4} = 2 ^{4} x ^{4} = 16 *x* ^{4}

4. (3( *x* –4)) ^{2} = 3 ^{2} ( *x* –4) ^{2} = 9( *x* –4) ^{2}

5. 6(2 *x* ) ^{3} = 6(2 ^{3} x ^{3} )= 6(8 *x* ^{3} )= 48 *x* ^{3}

6. 6y ^{2} (3y ^{4} ) ^{2} = 6y ^{2} (3 ^{2} (y ^{4} ) ^{2} )= 6y ^{2} (9y ^{8} )= 54y ^{10}

7. (5 *x* ^{2} y ^{4} z ^{6} ) ^{2} = 5 ^{2} ( *x* ^{2} ) ^{2} (y ^{4} ) ^{2} (z ^{6} ) ^{2} = 25 *x* ^{4} y ^{8} z ^{12}

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