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To evaluate an expression with variables:

1. Substitute the values for the variables.

2. Identify grouping symbols, beginning with the innermost symbols.

3. Determine and apply the rules of exponents to simplify.

4. Evaluate.

Evaluate the expression using x = –1 and y=3.
(6x4y3)

What is the value of the expression?
–162
–54
162
216

1 answer

To evaluate the expression \( 6x^4y^3 \) using \( x = -1 \) and \( y = 3 \), we will follow the steps outlined:

  1. Substitute the values for the variables: \[ 6(-1)^4(3)^3 \]

  2. Identify grouping symbols:
    There are no additional grouping symbols to worry about since the expression is straightforward.

  3. Determine and apply the rules of exponents:

    • First, calculate \( (-1)^4 \): \[ (-1)^4 = 1 \]
    • Next, calculate \( (3)^3 \): \[ (3)^3 = 27 \]

    Now substitute these results back into the expression: \[ 6 \cdot 1 \cdot 27 \]

  4. Evaluate: \[ 6 \cdot 27 = 162 \]

Thus, the value of the expression \( 6x^4y^3 \) when \( x = -1 \) and \( y = 3 \) is \( \boxed{162} \).