Naloge

8.

Izračunaj vrednosti izrazov naprej brez uporabe računala, nato pa z računalom.

a) $\displaystyle\left(\frac{4}{7}\right)^{-3}-\left(\frac{7}{8}\right)^{2}+\left(1-\frac{5}{7}\right)^{-3}$

b) $\displaystyle\left(\frac{5}{81}\right)^{-1}\cdot\left(\left(\frac{9}{5}\right)^{-2}+\left(\frac{5}{18}\right)^2\right)$

c) $\displaystyle\left(2\frac{1}{3}\right)^3\cdot\left(2\frac{4}{7}\right)^3$

č) $\displaystyle\left(\frac{3}{4}\right)^2\cdot\left(\frac{16}{81}\right)^2\cdot\left(\frac{27}{64}\right)^2$

K rezultatom vpiši črko naloge, ki ji rezultat pripada.

$\frac{1}{256}$

$6 \frac{1}{4}$

$216$

$47\frac{15}{32}$

č

b

c

a

9.

Primerjaj vrednosti naslednjih številskih izrazov.
a) $\displaystyle \frac{12^0+\left( \frac{2}{3} \right) ^{-3}\cdot \left( \frac{3}{4} \right) ^{-3}} {(3^{-1}-(-3)^{-3})^{-1}}$ b) $\displaystyle \frac{\left( \frac{4}{5} \right) ^{-3}-(-3)^0\cdot \left( \frac{3}{4} \right) ^3} {2-(-5)^{-2}}$
Kateri izraz ima večjo vrednost? Nalogo reši najprej brez uporabe računala, nato pa z računalom.

10.

11.

12.

Poenostavi izraze.

a) $\displaystyle (2x^{-1}y^3)^2\cdot (-2x^4y^{-2})^3= $ -32 $x$ ¹⁰ $y$ ⁰

b) $\displaystyle (7a^2b^3c^{-4})^2\cdot(5a^{-3}c^2)^3:(5a^{-1})^5=$

49

25

$b$ ⁶ $c$ ^-2

c) $\displaystyle \left(\frac{x^2}{5y}\right)^3\cdot\left(\frac{2y^2}{x}\right)^4:\left(\frac{4y^2}{5x}\right)^2=$

1

5

$x$ ⁴ $y$ ¹

č) $\displaystyle \left(\frac{x^2}{y^3}\right)^2\cdot\left(\frac{y^2}{x^3}\right)^3:\left(x^{-5}\right)^2=$ $x$ ⁵

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