Which expression is equivalent to start fraction, 5, to the power minus 1 , divided by, 5, to the power minus 2 , end fraction, dot, 5, to the power minus 3 , question mark
5
−2
5
−1
⋅5
−3
?
Answer
Multiple Choice Answers
5, to the power 45
4
5, to the power minus 25
−2
5, to the power minus 45
−4
11
The expression can be simplified using the properties of exponents. When dividing two numbers with the same base, you subtract the exponents.
So, 5 to the power -1 divided by 5 to the power -2 is equivalent to 5 to the power (-1 - (-2)).
5 to the power (-1 - (-2)) is equal to 5 to the power (-1 + 2), which simplifies to 5 to the power 1.
Finally, multiplying 5 to the power 1 by 5 to the power -3 is equivalent to adding the exponents, which gives us 5 to the power (1 - 3), or 5 to the power -2.
Therefore, the expression is equivalent to 5 to the power -2, which is represented as 5^-2.
The correct answer is 5, to the power minus 2.
Which expression is equivalent to left bracket, 2, to the power 5 , right bracket, to the power 0 , dot, 2, to the power 0 , question mark(2
5
)
0
⋅2
0
?
Answer
Multiple Choice Answers
00
11
3232
22
The expression can be simplified using the property of any number raised to the power of 0 equals 1.
So, 2 to the power 5 raised to the power 0 is equal to 1 multiplied by 2 to the power 0.
Any number raised to the power of 0 is 1, so 2 to the power 0 is equal to 1.
Therefore, the expression simplifies to 1 multiplied by 1, which is equal to 1.
The correct answer is 11.
Which expression is equivalent to left bracket, 2, to the power minus 3 , right bracket, to the power 0 , times, 2, to the power minus 2 , question mark(2
−3
)
0
×2
−2
?
Answer
Multiple Choice Answers
88
00
one half
2
1
one quarter
4
1
The expression can be simplified using the property of any number raised to the power of 0 equals 1.
So, 2 to the power -3 raised to the power 0 is equal to 1 multiplied by 2 to the power -2.
To simplify 2 to the power -2, we can use the property of negative exponents, which states that a number raised to a negative exponent is equal to 1 divided by the number raised to the positive exponent.
So, 2 to the power -2 is equal to 1 divided by 2 to the power 2, which is 1 divided by 4.
Therefore, the expression simplifies to 1 multiplied by 1/4, which is equal to 1/4 or one quarter.
The correct answer is one quarter.
To simplify the given expression, we can use the rule of exponents that states when dividing two numbers with the same base, we subtract the exponents.
So, we have:
(start fraction, 5, to the power minus 1, end fraction) divided by (5, to the power minus 2) multiplied by 5, to the power minus 3.
Using the exponent rule, we subtract the exponents:
5^(-1) / 5^(-2) * 5^(-3) = 5^(-1 - (-2)) * 5^(-3) = 5^1 * 5^(-3) = 5^(-2)
Therefore, the expression is equivalent to 5^(-2). Hence, the correct answer is "5, to the power minus 25."
To find the equivalent expression, we can use the rules of exponents. The rule states that when dividing two numbers with the same base, you subtract the exponents.
In this case, we have (5^(-1))/(5^(-2)) * 5^(-3).
To subtract the exponents for the fraction, we have -1 - (-2), which simplifies to -1 + 2 = 1.
So the fraction becomes 5^1.
For the second part, we have 5^(-3).
Now we can multiply the two expressions together to get the final answer.
5^1 * 5^(-3) equals 5^(1 - 3), which simplifies to 5^(-2).
Therefore, the equivalent expression is 5^(-2).
The correct option is "5, to the power minus 25."