Apply the product rule of integer exponents to find the numerical equivalent of 12−5⋅127 . Show your work and explain how you used the product rule of integer exponents.(2 points)
To apply the product rule of integer exponents to find the numerical equivalent of 12^(-5) * 127, we first need to understand the rule.
The product rule of integer exponents states that when multiplying numbers with the same base but different exponents, you can add the exponents and keep the base the same.
In this case, we have 12^(-5) * 127. The base is 12 and the exponents are -5 and 1.
Using the product rule of integer exponents, we add the exponents:
12^(-5) * 127 = 12^(-5+1) * 127
Since -5+1 equals -4, we can rewrite the expression as:
12^(-5) * 127 = 12^(-4) * 127
Now, to find the numerical equivalent, we calculate 12^(-4):
12^(-4) = 1 / 12^4 = 1 / 20736 = 0.000048
Now we can multiply this result by 127:
0.000048 * 127 = 0.006096
Therefore, the numerical equivalent of 12^(-5) * 127 is 0.006096.
By applying the product rule of integer exponents, we were able to simplify the expression and find the numerical value.
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To apply the product rule of integer exponents to find the numerical equivalent of 12^(-5) * 127, we need to remember that the product rule states that when multiplying two terms with the same base, you add the exponents.
First, let's break down the given expression: 12^(-5) * 127.
12^(-5) can be expressed as 1/(12^5) since a negative exponent represents the reciprocal of the positive exponent.
Now, let's substitute this back into the expression: 1/(12^5) * 127.
To find the numerical equivalent, we need to evaluate each exponent separately.
12^5 equals 12 * 12 * 12 * 12 * 12, which is equal to 248,832.
Now, substituting this back into the expression: 1/248,832 * 127.
To multiply a fraction and a whole number, we simply multiply the numerator and denominator with the whole number.
1 * 127 = 127
Therefore, the numerical equivalent of 12^(-5) * 127 is 127/248,832.
To apply the product rule of integer exponents, we need to understand what the rule states. The product rule of integer exponents states that if we have the same base raised to different exponents being multiplied together, we can combine them by adding the exponents.
In this case, we have 12^(-5) multiplied by 12^7.
To find the numerical equivalent, we can calculate each of the exponents separately and then multiply the results together.
First, let's find 12^(-5). The negative exponent indicates that we need to take the reciprocal of the base raised to the positive exponent. In this case, 12^(-5) is equal to 1/12^5.
Now, let's find 12^7. This is a positive exponent, so we simply calculate 12 raised to the power of 7.
12^7 = 12 * 12 * 12 * 12 * 12 * 12 * 12 = 35,831,808.
Now, to find the numerical equivalent of the expression 12^(-5) * 12^7, we multiply the values we found:
1/12^5 * 35,831,808 = 1/248,832 * 35,831,808 = 143/497,664.
Therefore, the numerical equivalent of 12^(-5) * 12^7 is 143/497,664.
We used the product rule of integer exponents by multiplying two terms with the same base (12) but different exponents (-5 and 7). By adding the exponents (-5 + 7) we obtained a simplified expression before evaluating it numerically.