First, try 99^3 = 970299; therefore, it is not the least possible value.
The above number is a multiple of 99, so we can factor this out to find the least possible value. So we try to factor 99:
99 = 9 * 11
99 = 3^2 * 11^ 1
and 3^3 * 11^3 = 35937
The least possible value is 4^1 + 11^2 = 125. Its sum is 125 which is a perfect cube.
First, find the scale factor.
8.4 / 7 = 1.2
9 / 7.5 = 1.2
7.2 / 6 = 1.2
Since both solids are different sizes, the solids aren't congruent.
The size ratio for all the sides are:
8.4:7
9:7.5
7.2:6
Since the scale factor isn't 1:1 this also proves that the solids are NOT congruent.
Since both solids are the same kind of shape and have an identical scale factor, the solids are similar.
Best of Luck!
Looking at the question we can see that it says:
We should know what these symbols mean:
stands for something less than the other, for example:
We can say that 2 is less than 5 so in a symbolic form it can be written as,
Similarly,
stands for something greater than the other, for example:
We can say that 7 is greater than 5, in a symbolic form it can be written as,
So here, means that, 42153 is greater than 35214.
(
3
x
3
2
y
3
x
2
y
−
1
2
)
−
2
(
3
x
3
2
y
3
x
2
y
-
1
2
)
-
2
Move
x
3
2
x
3
2
to the denominator using the negative exponent rule
b
n
=
1
b
−
n
b
n
=
1
b
-
n
.
⎛
⎝
3
y
3
x
2
y
−
1
2
x
−
3
2
⎞
⎠
−
2
(
3
y
3
x
2
y
-
1
2
x
-
3
2
)
-
2
Multiply
x
2
x
2
by
x
−
3
2
x
-
3
2
by adding the exponents.
Tap for more steps...
(
3
y
3
x
1
2
y
−
1
2
)
−
2
(
3
y
3
x
1
2
y
-
1
2
)
-
2
Move
y
−
1
2
y
-
1
2
to the numerator using the negative exponent rule
1
b
−
n
=
b
n
1
b
-
n
=
b
n
.
(
3
y
3
y
1
2
x
1
2
)
−
2
(
3
y
3
y
1
2
x
1
2
)
-
2
Multiply
y
3
y
3
by
y
1
2
y
1
2
by adding the exponents.
Tap for more steps...
⎛
⎝
3
y
7
2
x
1
2
⎞
⎠
−
2
(
3
y
7
2
x
1
2
)
-
2
Change the sign of the exponent by rewriting the base as its reciprocal.
⎛
⎝
x
1
2
3
y
7
2
⎞
⎠
2
(
x
1
2
3
y
7
2
)
2
Use the power rule
(
a
b
)
n
=
a
n
b
n
(
a
b
)
n
=
a
n
b
n
to distribute the exponent.
Tap for more steps...
(
x
1
2
)
2
3
2
(
y
7
2
)
2
(
x
1
2
)
2
3
2
(
y
7
2
)
2
Simplify the numerator.
Tap for more steps...
x
3
2
(
y
7
2
)
2
x
3
2
(
y
7
2
)
2
Simplify the denominator.
Tap for more steps...
x
9
y
7
Try 488 or 3050 but I think it is most likely 488.