Product Rule of Exponents Quick Check
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Question
Find the numerical equivalent of 49⋅4−7(1 point)
Responses
16
16
416
4 superscript 16 baseline
42
4 squared
4
0.0014
Find the numerical equivalent of 49⋅4−7(1 point)
Responses
16
16
416
4 superscript 16 baseline
42
4 squared
4
The numerical equivalent of 49⋅4^(-7) is 0.000000124.
To find the numerical equivalent of 49⋅4−7, let's break it down step-by-step:
Step 1: Calculate 49.
49 = 7² = 7 * 7 = 49
Step 2: Calculate 4^-7.
Recall that a negative exponent is equivalent to 1 divided by the positive exponent. Therefore, 4^-7 is equal to 1/4^7.
1/4^7 = 1/(4 * 4 * 4 * 4 * 4 * 4 * 4) = 1/16384
Step 3: Multiply 49 by 1/16384.
49 * 1/16384 = 49/16384
So, the numerical equivalent of 49⋅4^-7 is 49/16384.
To find the numerical equivalent of the expression 49⋅4^(-7), we can use the product rule of exponents. The product rule states that when multiplying two numbers with the same base, you can add the exponents. In this case, the base is 4.
Step 1: Start with the base, which is 4.
Step 2: Multiply the base by itself 9 times since the exponent is 9 (4^9).
Step 3: Divide the result by 4^7 because the exponent is -7 (4^9 / 4^7).
Step 4: Simplify the expression by subtracting the exponents: 4^(9 - 7).
Step 5: Simplify further by subtracting the exponents: 4^2.
So the numerical equivalent of 49⋅4^(-7) is 4^2, which is equal to 16. Hence, the correct response is "16".