is this how you simplify exponents and integers:
10+4^3x2^-2
10+ 1/64 + 1/4
1/64 + 1/4= 1/256
10 + 1/256= 10 1/256
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ever since I learn this in class, I'm getting more confuse because I keep receiving fraction as an answer.can you tutor me on this lesson?
What you are doing is to the negative power. 4^3 is 64, not 1/64. however,2^-2 is 1/4 because it is a negative power.
10 + 4^3 x 2^-2
10 + 64 x 1/4
10 + 16
26
Just remember, a positive exponent is integer x integer as many times as the number indicated by the exponent. A negative exponent is the exact same thing, except the number you get will be the denominator and your numerator will be 1.
ooooooooooh!!!!!! thank you! but what will happen if the numberator cannot be divided by the denominator?
Of course! I'd be happy to help you understand how to simplify expressions with exponents and integers.
To simplify an expression with exponents and integers, we follow the order of operations (PEMDAS):
1. First, we evaluate any exponents in the expression. In this case, we have 4^3 and 2^-2.
4^3 means 4 raised to the power of 3, which is equal to 4 x 4 x 4 = 64.
2^-2 means 2 raised to the power of -2, which is equal to 1 divided by 2 x 2 = 1/4.
So, our expression becomes: 10 + 64 x 1/4.
2. Next, we perform any multiplication or division from left to right. In this case, we have 64 x 1/4.
To multiply fractions, we multiply the numerators together and multiply the denominators together. So, 64 x 1/4 is equal to (64 x 1) / (1 x 4) = 64/4 = 16.
Our expression becomes: 10 + 16.
3. Lastly, we perform any addition or subtraction from left to right. In this case, we have 10 + 16.
Adding 10 and 16 gives us a final result of 26.
So, after simplifying the expression 10 + 4^3 x 2^-2, we get the answer 26.
If you're getting fractions as answers, it could be because there are fractions involved in the original expression or because you made an error during the calculations. Double-check your work to ensure you're performing the operations correctly at each step.