Simplify: (5d3)(-2d2)

Frank & Gardner Math 8 Multiplying Monomials Quiz 1

1. Simplify: (m⁴)²

To simplify (m4)2, we need to apply the exponent of 2 to the expression inside the parentheses. This means we need to multiply the exponent of 2 to both the base m and the exponent 4. Multiplying the exponents gives us m8, so the simplified expression is m8.

Explanation

To simplify (m4)2, we need to apply the exponent of 2 to the expression inside the parentheses. This means we need to multiply the exponent of 2 to both the base m and the exponent 4. Multiplying the exponents gives us m8, so the simplified expression is m8.

2. Simplify: (n⁵)(n²)(m³)(m⁴)

The given expression can be simplified by multiplying the like terms together. Since n is raised to the power of 5 and 2, and m is raised to the power of 3 and 4, we can add the exponents of n and m separately. This gives us n^7 * m^7 as the simplified form of the expression.

Explanation

The given expression can be simplified by multiplying the like terms together. Since n is raised to the power of 5 and 2, and m is raised to the power of 3 and 4, we can add the exponents of n and m separately. This gives us n^7 * m^7 as the simplified form of the expression.

3. Simplify: (5d³)(-2d²)

10

-10

10

-10

The expression (5d3)(-2d2) can be simplified by multiplying the coefficients and adding the exponents. In this case, 5 multiplied by -2 gives -10, and 3 added to 2 gives 5. Therefore, the simplified expression is -10d5.

Explanation

The expression (5d3)(-2d2) can be simplified by multiplying the coefficients and adding the exponents. In this case, 5 multiplied by -2 gives -10, and 3 added to 2 gives 5. Therefore, the simplified expression is -10d5.

4. Simplify: (

1 fourth

c d cubed

right parenthesis squared

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Explanation

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5. Simplify: 5x²(5²x³)

The expression 5x2(52x3) can be simplified using the order of operations, which states that we should perform any calculations inside parentheses first. In this case, we have the expression 52x3 inside the parentheses. Multiplying 52 by 3 gives us 156. Next, we multiply this result by 5x2, which is equivalent to multiplying 156 by 10. Therefore, the simplified expression is 1560.

Explanation

The expression 5x2(52x3) can be simplified using the order of operations, which states that we should perform any calculations inside parentheses first. In this case, we have the expression 52x3 inside the parentheses. Multiplying 52 by 3 gives us 156. Next, we multiply this result by 5x2, which is equivalent to multiplying 156 by 10. Therefore, the simplified expression is 1560.